Our primary objective is to utilize the "molecular clock hypothesis" to develop mathematical models that will allow us to study how cancers grow and spread. Human cancer growth cannot be directly observed and the overall goal is to develop an approach that can retrospectively reconstruct tumor progression by "reading" the ancestry surreptitiously written within genomes by replication errors. Sequences are commonly used to reconstruct the genealogy of species and individuals, and we propose to translate this general molecular phylogeny approach to human cancers. We will use DNA methylation data, an epigenetic modification of DNA that is replicated at cell division. As direct calculation can be either impractical or infeasible, we propose to use rejection algorithms, a simulation-based approach. This general framework will allow us to estimate the age of a tumor, the age of a metastasis, the methylation error rate, and whether the metastasis is derived from a specific population of cells from the primary cancer. Our aims are motivated by ongoing studies at the Norris Comprehensive Cancer Center at the University of Southern California. Specifically, we propose to: 1. Develop methods that will allow us to estimate parameters characterizing the growth of cancer using 5'to 3'DNA methylation patterns and validate these models using clinical data from patients and experimental data from cancer cell lines. The models will address the following biological problems: a. Estimate the number of cancer stem cells based on the types of ancestral trees inferred from the methylation patterns;b. Evaluate tumor heterogeneity, e.g. identify different subpopulations of cells in the left and right side of the tumor;c. Estimate tumor age and the rate at which methylation errors occur. 2. Extend the models developed in Aim 1 to include additional complexities. We propose to address the following: a. Modeling multiple gene regions within a single ancestral tree;b. Modeling autosomal genes (diploid genomes);c. Modeling multiple tissues (primary tumor and metastasis), to answer questions about whether the cell populations are the same age, or if one is younger and derived from the other;We will apply the methods developed in Aims 1-2 to DNA methylation patterns observed in primary tumors of the colon and distant metastasis in humans. PUBLIC HEALTH RELEVANCE: Cancer is the second leading cause of death in the United States in 2005, as reported by the National Center for Health Statistics. Its treatment relies on understanding how cancers grow and spread. We propose to develop mathematical models that can retrospectively reconstruct tumor histories, allowing us to address important biological questions about the growth and spread of cancer.